The regular spaces with countably based models

Authors:
Keye Martin
Affiliations:
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
Venue:
Theoretical Computer Science - Topology in computer science
Year:
2003

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Abstract

The regular spaces which may be realized as the set of maximal elements in an ω-continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces. These results enable us to prove that the probabilistic powerdomain of a countably based model of a metric space always contains a copy of the normalized Borel measures in their weak topology, and to establish the hierarchy for countably based models.